Spatial Analysis of Gravity Data in the Basement of the Yaoundé-Yoko Area from the Global Gravity Model: Implication on the Sanaga Fault (South-Cameroon)

In this work, gravity anomalies from the XGM2016 global gravity model are used to study the basement of the Yaounde, Yoko area. The aim is to locate the characteristic tectonic faults and to characterize the geometry of the basement of these localities in order to improve the knowledge of the structural and tectonic basement of the study area. Numerical filters (vertical gradient, horizontal gradient, upward continuation) and Euler deconvolution were applied to the gravity anomalies respectively for qualitative and quantitative analysis. The results of the qualitative analysis allowed us to establish the lineament map of the study area;ranging from 0 to 35 km depth. For the quantitative analysis, the work is done in two parts: 1) highlighting the distribution of depths of geological structures in the basement of the study area;2) 2D1/2 modeling of geological structures to highlight the geometry of the basement of Yaounde, Yoko area. Thus, from five suitably selected profiles, the established models reveal the presence of eight blocks of geological structures of different densities and analyze their implications on the Sanaga Fault. Moreover, the models show that the positive anomalies characteristics for the Sanaga Fault reflect the anomalous character due to the strong dominance of the shale intrusion in the basement.

Spatial-temporal Evolution and Determinants of the Belt and Road Initiative: A Maximum Entropy Gravity Model Approach

The spatial interaction model is an effective way to explore the geographical disparities inherent in the Belt and Road Initiative(BRI) by simulating spatial flows. The traditional gravity model implies the hypothesis of equilibrium points without any reference to when or how to achieve it. In this paper, a dynamic gravity model was established based on the Maximum Entropy(MaxEnt) theory to estimate and monitor the interconnection intensity and dynamic characters of bilateral relations. In order to detect the determinants of interconnection intensity, a Geodetector method was applied to identify and evaluate the determinants of spatial networks in five dimensions. The empirical study clearly demonstrates a heterogeneous and non-circular spatial structure. The main driving forces of spatial-temporal evolution are foreign direct investment, tourism and railway infrastructure construction, while determinants in different sub-regions show obvious spatial differentiation. Southeast Asian countries are typically multi-island area where aviation infrastructure plays a more important role. North and Central Asian countries regard oil as a pillar industry where power and port facilities have a greater impact on the interconnection. While Western Asian countries are mostly influenced by the railway infrastructure, Eastern European countries already have relatively robust infrastructure where tariff policies provide a greater impetus.

A novel method for identifying influential nodes in complex networks based on gravity model

How to identify influential nodes in complex networks is an essential issue in the study of network characteristics.A number of methods have been proposed to address this problem,but most of them focus on only one aspect.Based on the gravity model,a novel method is proposed for identifying influential nodes in terms of the local topology and the global location.This method comprehensively examines the structural hole characteristics and K-shell centrality of nodes,replaces the shortest distance with a probabilistically motivated effective distance,and fully considers the influence of nodes and their neighbors from the aspect of gravity.On eight real-world networks from different fields,the monotonicity index,susceptible-infected-recovered(SIR)model,and Kendall’s tau coefficient are used as evaluation criteria to evaluate the performance of the proposed method compared with several existing methods.The experimental results show that the proposed method is more efficient and accurate in identifying the influence of nodes and can significantly discriminate the influence of different nodes.

Energy Conditions and Constraints on the Generalized Non-Local Gravity Model

We study and derive the energy conditions in generalized non-local gravity, which is the modified theory of general relativity obtained by adding a term m2n-2R□-nRto the Einstein-Hilbert action. Moreover, to obtain some insight on the meaning of the energy conditions, we illustrate the evolutions of four energy conditions with the model parameter ε for different n. By analysis we give the constraints on the model parameters ε.

A GOCE only gravity model GOSG01S and the validation of GOCE related satellite gravity models

We compile the GOCE-only satellite model GOSG01S complete to spherical harmonic degree of 220 using Satellite Gravity Gradiometry （SGG） data and the Satellite-to-Satellite Tracking （SST） observations along the GOCE orbit based on applying a least-squares analysis. The diagonal components （Vxx, Vyy, Vzz） of the gravitational gradient tensor are used to form the system of observation equations with the band-pass ARMA filter. The point-wise acceleration observations （ax, ay, az） along the orbit are used to form the system of observation equations up to the maximum spherical harmonic degree/order 130. The analysis of spectral accuracy characteristics of the newly derived gravitational model GOSG01S and the existing models GOTIM04S, GODIR04S, GOSPW04S and JYY_GOCE02S based on their comparison with the ultrahigh degree model EIGEN-6C2 reveals a significant consistency at the spectral window approximately between 80 and 190 due to the same period SGG data used to compile these models. The GOCE related satellite gravity models GOSG01S, GOTIM05S, GODIR05S, GOTIM04S, GODIR04S, GOSPW04S, JYY_- GOCE02S, EIGEN-6C2 and EGM2008 are also validated by using GPS-leveling data in China and USA. According to the truncation at degree 200, the statistic results show that all GGMs have very similar differences at GPS-leveling points in USA, and all GOCE related gravity models have better performance than EGM2008 in China. This suggests that all these models provide much more information on the gravity field than EGM2008 in areas with low terrestrial gravity coverage. And STDs of height anomaly differences in China for the selected truncation degrees show that GOCE has improved the accuracy of the global models beyond degree 90 and the accuracies of the models improve from 24 cm to 16 cm. STDs of geoid height differences in USA show that GOSG01S model has best consistency comparing with GPSleveling data for the frequency band of the degree between 20 and 160.

The construction of high precision geostrophic currents based on new gravity models of GOCE and satellite altimetry data

The new gravity field models of gravity field and steady-state ocean circulation explorer(GOCE),TIM_R6 and DIR_R6,were released by the European Space Agency(ESA)in June 2019.The sixth generation of gravity models have the highest possible signal and lowest error levels compared with other GOCE-only gravity models,and the accuracy is significantly improved.This is an opportunity to build high precision geostrophic currents.The mean dynamic topography and geostrophic currents have been calculated by the 5th(TIM_R5 and DIR_R5),6th(TIM_R6 and DIR_R6)release of GOCE gravity field models and ITSG-Grace2018 of GRACE gravity field model in this study.By comparison with the drifter results,the optimal filtering lengths of them have been obtained(for DIR_R5,DIR_R6,TIM_R5 and TIM_R6 models are 1°and for ITSG-Grace2018 model is 1.1°).The filtered results show that the geostrophic currents obtained by the GOCE gravity field models can better reflect detailed characteristics of ocean currents.The total geostrophic speed based on the TIM_R6 model is similar to the result of the DIR_R6 model with standard deviation(STD)of 0.320 m/s and 0.321 m/s,respectively.The STD of the total velocities are 0.333 m/s and 0.325 m/s for DIR_R5 and TIM_R5.When compared with ITSG-Grace2018 results,the STD(0.344 m/s)of total geostrophic speeds is larger than GOCE results,and the accuracy of geostrophic currents obtained by ITSG-Grace2018 is lower.And the absolute errors are mainly distributed in the areas with faster speeds,such as the Antarctic circumpolar circulation,equatorial region,Kuroshio and Gulf Stream areas.After the remove-restore technique was applied to TIM_R6 MDT,the STD of total geostrophic speeds dropped to 0.162 m/s.

Time-varying gravity field model of Sichuan-Yunnan region based on the equivalent mass source model

High-precision time-varying gravity field is an effective way to study the internal mass movement and understanding the spatio-temporal evolution process of the geodynamic system.Compared to the satellite gravity measurement,the repeated terrestrial gravity observation can provide a more high-order signal related to the shallow crust and subsurface.However,the suitable and unified method for gravity model estimation is a key problem for further applications.In this study,we introduce the spherical hexahedron element to simulate the field source mass and forward model the change of gravity field located at the Sichuan-Yunnan region(99—104°E,23—29°N)in the four epochs from 2015 to 2017.Compared to the experimental results based on Slepian or spherical harmonics frequency domain method,this alternative approach is suitable for constructing the equivalent mass source model of regional-scale gravity data,by introducing the first-order smooth prior condition of gravity time-varying signal to suppress the high-frequency component of the signal.The results can provide a higher spatial resolution reference for regional gravity field modeling in the Sichuan-Yunnan region.

A Study on Transport Costs and China＇s Exports： An Extended Gravity Model

This paper suggests an extending conventional gravity model design to empirically analyze the effect of transport costs and port efficiency on China's export flows. It shows that factor endowment and transport costs variables affect export trade value in directions that New Trade Theory(NTT) predicted. Also, the evidence indicates that, controlling for the effects of transport costs on trade, variables in traditional gravity model are consistent with previous empirical studies in both magnitudes and directions. Moreover, more than 22% of the variation in Chinese export trade can be explained by those three variables alone. The findings reported in this paper empirically explains how seriously transport costs and port efficiency affect China's export growth by comparing effects of labour production factor costs on external trade. It suggests that the improvement of port efficiency and reduction of road transport costs play a vital role in China's export competitiveness in the global market.

The relationship between China and regional economic agreement in global value chain:An analysis based on gravity model

Global value chain has become a new and dominant pattern of international division of labor in the world.Meanwhile,international cooperation has turned from multilateralism to regionalization.This paper intends to use gravity model to explore the connections between the two trajectories.As a political and economic major power in the world,China should set about employing a comprehensive,self-oriented and well-functioning strategy of regional economic integration,either out of considerations for its global and regional strategies or the need to transform economic development model.In the process of implementation,China should be selective in choosing partners,choosing competitive ones at different levels of the global value chain.

The impacts of China’s economic policies on Sino-African agricultural trade:evidence from the gravity model analysis

The rapid economic growth of China and some African countries provides tremendous opportunity for the agricultural trade.Both China and African countries have made great efforts in achieving win-win cooperation between the two economies.This paper aims to provide a comprehensive analysis of impacts of various factors on bilateral agricultural trade between China and Africa.The fixed effect Gravity model is adopted in the study to assess the impacts of different factors on Sino-African bilateral agricultural trade,based on the various data sets covering 1992-2010.The economic growth and rising agricultural production are found to be the two key factors to drive Sino-African future bilateral agricultural trade.Therefore,the focus should be put on the long-run effects of investment in promoting bilateral agricultural trade.Moreover,the agricultural cooperation should be enhanced to improve the agricultural production and fully use the comparative advantages in both sides.

A High-Resolution Earth’s Gravity Field Model SGG-UGM-2 from GOCE,GRACE,Satellite Altimetry,and EGM2008

This paper focuses on estimating a new high-resolution Earth’s gravity field model named SGG-UGM-2 from satellite gravimetry,satellite altimetry,and Earth Gravitational Model 2008(EGM2008)-derived gravity data based on the theory of the ellipsoidal harmonic analysis and coefficient transformation(EHA-CT).We first derive the related formulas of the EHA-CT method,which is used for computing the spherical harmonic coefficients from grid area-mean and point gravity anomalies on the ellipsoid.The derived formulas are successfully evaluated based on numerical experiments.Then,based on the derived least-squares formulas of the EHA-CT method,we develop the new model SGG-UGM-2 up to degree 2190 and order 2159 by combining the observations of the Gravity Field and Steady-State Ocean Circulation Explorer(GOCE),the normal equation of the Gravity Recovery and Climate Experiment(GRACE),marine gravity data derived from satellite altimetry data,and EGM2008-derived continental gravity data.The coefficients of degrees 251–2159 are estimated by solving the block-diagonal form normal equations of surface gravity anomalies(including the marine gravity data).The coefficients of degrees 2–250 are determined by combining the normal equations of satellite observations and surface gravity anomalies.The variance component estimation technique is used to estimate the relative weights of different observations.Finally,global positioning system(GPS)/leveling data in the mainland of China and the United States are used to validate SGG-UGM-2 together with other models,such as European improved gravity model of the earth by new techniques(EIGEN)-6C4,GECO,EGM2008,and SGG-UGM-1(the predecessor of SGG-UGM-2).Compared to other models,the model SGG-UGM-2 shows a promising performance in the GPS/leveling validation.All GOCE-related models have similar performances both in the mainland of China and the United States,and better performances than that of EGM2008 in the mainland of China.Due to the contribution of GRACE data and the new marine gravity anomalies,SGG-UGM-2 is slightly better than SGG-UGM-1 both in the mainland of China and the United States.

Crustal structure of the western Indian shield: Model based on regional gravity and magnetic data

Regional surface gravity data and global satellite magnetic data have been utilized to generate a preliminary model of the crustal structure along a southwest-northeast profile （Gadra-Fatehpur） through western Rajasthan.The study area represents the western part of the Indian continental landmass which has undergone several major episodes of repeated subduction/collision,plume traces and rifting from Archaean to recent times.The temporal and spatial relationship between the various geotectonic provinces is quite complex,thereby limiting the emergence of a suitable crustal structure model for this region.Exposures of the Malani Igneous Suite （MIS）,a product of bimodal volcanism （～780 Ma）,and considered to be the third largest felsic magmatic province of the world,is evident along the profile and also to the southwest of the study area.The easternmost part of the profile is close to the DAFB （Delhi Aravalli Fold Belt）,a Proterozoic orogenic belt.This study probes the geometry of the different crustal units in terms of density and susceptibility variations in order to decipher the imprints of the major tectonic processes the region has undergone.In order to decipher the crustal geometry of the Gadra-Fatehpur profile,two NW-SE gravity and magnetic profile vertical sections （A-A＇ in the south and B-B＇ in the north） are modelled on the basis of the constraints provided from previous seismic models.The crustal model of the Gadra-Fatehpur profile is composed of alluvium,Tertiary sediments,MIS,Marwar Supergroup,low-density layers （LDLs） and the middle-lower crustal layers,with a distinct change in configuration from the southwest to northeast.The Moho dips from SW to NE,the MIS in the SW gives way to the thick pile of the Marwar Supergroup to the NE.The evolution of MIS has been suggested to have occurred as a consequence of delamination of the upper mantle.LDLs are incorporated in Gadra-Fatehpur model.In the SW,LDL （2550 kg/m3） lies below the MIS in the NE,another LDL （2604 kg/m3） is depicted below the mid-crustal layer.

A Gravity Forward Modeling Method based on Multiquadric Radial Basis Function

It is one of the most important part to build an accurate gravity model in geophysical exploration.Traditional gravity modelling is usually based on grid method,such as difference method and finite element method widely used.Due to self-adaptability lack of division meshes and the difficulty of high-dimensional calculation.

A new high-precision gravity solid tidal model for Precision Gravity Measurement Facility

It is significant for establishing gravity datum to construct precise gravity solid tidal model,A simple method with relatively low performance is to interpolate tidal parameters from the global gravity solid tide models.A competitive approach is to determine local gravity solid tidal model by harmonic analysis using long-time serial gravity observations.In this paper a new high-precision gravity solid tidal model for Precision Gravity Measurement Facility is estimated from two co-site gravimeters in the cave laboratory using modern international standard data processing techniques,whose accuracy is evaluated further by comparing with previous publications.The results show that:(1)the determined gravity solid tidal models from two co-site gravimeters are in good agreement with each other,of which the maximum differences for amplitude factors and phase delays don’t exceed 0.01700%and 2.50990°,respectively.(2)the performance of the obtained gravity solid tidal model is 0.00411 for amplitude factors and 0.24120°for phase delays,which is a little better than that of previous publications using superconducting gravity data from Wuhan station.(3)our results and methods are corrective and effective.(4)our model is tiny different from that provided by Wuhan station,which implies that it is necessary to construct a gravity solid tidal model for Precision Gravity Measurement Facility,rather than just adopting existing models at Wuhan station.Our results are helpful in realizing the goal of Precision Gravity Measurement Facility.

Analysis of the Processes of Gravity in the Framework of Curvature of Space and the Substantiation of the New Model

The paper belongs to the sphere of quantum physics, physics of waves and physical fields, in particular—to the gravitation. Their study provides a better understanding of the problems of natural sciences at all levels, from elementary particles, to Universe as a whole. Therefore, the solution of these problems is an urgent and important task, which to the works of many generations of scientists of the world was dedicated. However, they have not been fully resolved. In well-known works, including general relativity, determination of the wave and energy parameters of the gravitational field of the Universe and their numerical values are absent. Solutions found are limited to tensor equations of a general form, which allows their interpretation of over a wide range. Other disadvantages of famous models are: 1) the voluminous world of the Universe reduced to the planes on which space objects and other objects move, sagging planes due to their own mass;2) signs of “top” and “bottom” of the system, which are not in the real Universe, just as they are not on Earth and not in the Solar system;3) the formation of “voids” between the object and the curved space and others. Main goals of the work to identify these contradictions and find ways to resolve them are performed. The main difference and the scientific novelty of the work performed are the justification of the gravity model based on a rigorous determination of the wave and energy parameters of the gravitational field of the Universe and their numerical values. The initial parameters of this worked—is the frequency oscillation νG of the waves of the gravitational field (Nastasenko’s constant) found in 2011. Research Results: Knowing νG can find all wave parameters of the gravitational field and their numerical values. The proposed new spatial-wave model of the action of gravity is based on the wave parameters of the gravitational fields of material objects. In the framework of their unity with electromagnetic fields, it reduces their structures to similar ones and eliminates the drawbacks of the previous model—of replaced gravity on curvature of space.

WHU-Grace01s:A new temporal gravity field model recovered from GRACE KBRR data alone

A new temporal gravity field model called WHU-Grace01s solely recovered from Gravity Recovery and Climate Experiment （GRACE） K-Band Range Rate （KBRR） data based on dynamic integral approach is presented in this paper. After meticulously preprocessing of the GRACE KBRR data, the root mean square of its post residuals is about 0.2 micrometers per second, and seventy-two monthly temporal solutions truncated to degree and order 60 are computed for the period from January 2003 to December 2008. After applying the combi- nation filter in WHU-Grace01s, the global temporal signals show obvious periodical change rules in the large-scale fiver basins. In terms of the degree variance, our solution is smaller at high degrees, and shows a good consistency at the rest of degrees with the Release 05 models from Center for Space Research （CSR）, GeoForschungsZentrum Potsdam （GFZ） and Jet Pro- pulsion Laboratory 0PL）. Compared with other published models in terms of equivalent water height distribution, our solution is consistent with those published by CSR, GFZ, JPL, Delft institute of Earth Observation and Space system （DEOS）, Tongji University （Tongji）, Institute of Theoretical Geodesy （ITG）, Astronomical Institute in University of Bern （AIUB） and Groupe de Recherche de Geodesie Spatiale （GRGS}, which indicates that the accuracy of WHU-Grace01s has a good consistency with the previously published GRACE solutions.

Moho depth inversion in the Tibetan Plateau from high-precision gravity data

The Tibetan Plateau(TP)is the youngest orogenic belt resulting from a continental collision on the Earth.It is a natural laboratory for studying continental dynamics,such as continental convergence,plate subduction,and plateau uplift.Investigating the deep structure of the TP has always been a popular issue in geological research.The Moho is the boundary between the crust and the mantle and therefore plays a crucial role in the Earth’s structure.Parameters such as depth and lateral variation,as well as the fine structure of the crust-mantle interface,reveal the lithospheric dynamics in the TP.Two methods are generally employed to study the Moho surface:seismic detection and gravity inversion.Seismic detection has the characteristic of high precision,but it is limited to a few cross-sectional lines and is quite costly.It is not suitable for and cannot be carried out over a large area of the TP.The Moho depth over a large area can be obtained through gravity inversion,but this method is affected by the nature of gravity data,and the accuracy of the inversion method is lower than that of seismic detection.In this work,a high-precision gravity field model was selected.The Parker-Oldenburg interface inversion method was used,within the constraints of seismic observations,and the Bott iteration method was introduced to enhance the inversion efficiency.The Moho depth in the TP was obtained with high precision,consistent with the seismic detection results.The research results showed that the shape of the Moho in the TP is complex and the variation range is large,reaching 60−80 km.In contrast with the adjacent area,a clear zone of sharp variation appears at the edge of the plateau.In the interior of the TP,the buried depth of the Moho is characterized by two depressions and two uplifts.To the south of the Yarlung Zangbo River,the Moho inclines to the north,and to the north,the Moho depresses downward,which was interpreted as the Indian plate subducting to the north below Tibet.The Moho depression on the north side of the Qiangtang block,reaching 72 km deep,may be a result of the southward subduction of the lithosphere.The Moho uplift of the Qiangtang block has the same strike as the Bangong−Nujiang suture zone,which may indicate that the area is compensated by a low-density and low-velocity mantle.

Analysis and Study on Spatial Gravity Center of PM_(2.5) and Population Scale

With the rapid development of urbanization construction in China,population and industries are rapidly gathering in cities,bringing about economic development and also causing a large number of environmental problems,among which PM_(2.5) is the most concerned.In this paper,a spatial gravity center model was used to systematically analyze the spatiotemporal distribution characteristics of PM_(2.5) and population scale in China from 1999 to 2016.Conclusions were as below:(1)there were significant regional differences in PM_(2.5) pollution from 1999 to 2016,characterized by a spatial distribution of"high in the north and low in the south,and high in the inland and low in the coastal areas".(2)Nationwide,there was a significant spatial mismatch between the gravity center of PM_(2.5) pollution and the gravity center of population scale,with the two centers showing a trend of reverse dislocation development.

Measuring Network Configuration of the Yangtze River Middle Reaches Urban Agglomeration:Based on Modified Radiation Model

The objective of this study is to develop a framework for re-examining and re-defining the classical concepts of spatial interaction and reorganization in the urban system.We introduce a modified radiation model for spatial interactions,coupled with migration big data,transport accessibility algorithm,and city competitiveness assessment for efficient distribution of the inter-city flow through the network.The Yangtze River Middle Reaches(YRMR)urban agglomeration(UA)is chosen as the case study region to systematically identify and measure its spatial configuration and to gain insights for other UAs‘sustainable development in China.The results are also compared with those computed by the classical gravity model to systematically discuss the applicability of spatial interaction laws and models,and related practical policies for regional sustainable development are discussed based on the findings as well.The conclusions are highlighted below:1)Combining with the?city network paradigm‘and?central place theory‘can better express the spatial configurations of city systems in the context of?space of flows‘;2)The results validate the potentialities of a multi-analysis framework to assess the spatial configurations of city network based on the improved radiation model and network analysis tools;3)The applications of spatial interaction models should be considered according to the specific geographical entity and its spatial scale.

Monthly gravity field recovery from GRACE orbits and K-band measurements using variational equations approach

The Gravity Recovery and Climate Experiment（GRACE） mission can significantly improve our knowledge of the temporal variability of the Earth＇s gravity field.We obtained monthly gravity field solutions based on variational equations approach from GPS-derived positions of GRACE satellites and K-band range-rate measurements.The impact of different fixed data weighting ratios in temporal gravity field recovery while combining the two types of data was investigated for the purpose of deriving the best combined solution.The monthly gravity field solution obtained through above procedures was named as the Institute of Geodesy and Geophysics（IGG） temporal gravity field models.IGG temporal gravity field models were compared with GRACE Release05（RL05） products in following aspects：（i） the trend of the mass anomaly in China and its nearby regions within 2005-2010; （ii） the root mean squares of the global mass anomaly during 2005-2010; （iii） time-series changes in the mean water storage in the region of the Amazon Basin and the Sahara Desert between 2005 and 2010.The results showed that IGG solutions were almost consistent with GRACE RL05 products in above aspects（i）-（iii）.Changes in the annual amplitude of mean water storage in the Amazon Basin were 14.7 ± 1.2 cm for IGG,17.1 ± 1.3 cm for the Centre for Space Research（CSR）,16.4 ± 0.9 cm for the GeoForschungsZentrum（GFZ） and 16.9 ± 1.2 cm for the Jet Propulsion Laboratory（JPL） in terms of equivalent water height（EWH）,respectively.The root mean squares of the mean mass anomaly in Sahara were 1.2 cm,0.9 cm,0.9 cm and 1.2 cm for temporal gravity field models of IGG,CSR,GFZ and JPL,respectively.Comparison suggested that IGG temporal gravity field solutions were at the same accuracy level with the latest temporal gravity field solutions published by CSR,GFZ and JPL.